Survivable Network, Linear Programming Relaxations and the Parsimonious Property
We consider the survivable network design problem - the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-connected network design problem. We establish a...
| Main Authors: | , |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology, Operations Research Center
2004
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| Online Access: | http://hdl.handle.net/1721.1/5175 |
| _version_ | 1811083006219124736 |
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| author | Goemans, Michel X. Bertsimas, Dimitris J. |
| author_facet | Goemans, Michel X. Bertsimas, Dimitris J. |
| author_sort | Goemans, Michel X. |
| collection | MIT |
| description | We consider the survivable network design problem - the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem. |
| first_indexed | 2024-09-23T12:17:37Z |
| format | Working Paper |
| id | mit-1721.1/5175 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:17:37Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/51752019-04-12T13:40:42Z Survivable Network, Linear Programming Relaxations and the Parsimonious Property Goemans, Michel X. Bertsimas, Dimitris J. We consider the survivable network design problem - the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem. 2004-05-28T19:26:31Z 2004-05-28T19:26:31Z 1990-06 Working Paper http://hdl.handle.net/1721.1/5175 en_US Operations Research Center Working Paper;OR 216-90 1824527 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Goemans, Michel X. Bertsimas, Dimitris J. Survivable Network, Linear Programming Relaxations and the Parsimonious Property |
| title | Survivable Network, Linear Programming Relaxations and the Parsimonious Property |
| title_full | Survivable Network, Linear Programming Relaxations and the Parsimonious Property |
| title_fullStr | Survivable Network, Linear Programming Relaxations and the Parsimonious Property |
| title_full_unstemmed | Survivable Network, Linear Programming Relaxations and the Parsimonious Property |
| title_short | Survivable Network, Linear Programming Relaxations and the Parsimonious Property |
| title_sort | survivable network linear programming relaxations and the parsimonious property |
| url | http://hdl.handle.net/1721.1/5175 |
| work_keys_str_mv | AT goemansmichelx survivablenetworklinearprogrammingrelaxationsandtheparsimoniousproperty AT bertsimasdimitrisj survivablenetworklinearprogrammingrelaxationsandtheparsimoniousproperty |